Related papers: A generalization of intertwining operators for ver…
We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras $A_{k}(sl(2))$ for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible modules are…
In the present paper we construct explicitly the intertwining differential operators for the Jacobi algebra ${\cal G}_2.$ For the construction we use the singular vectors of the Verma modules over ${\cal G}_2$ which we have constructed…
Within the framework of the discrete Wess-Zumino-Novikov-Witten theory we analyze the structure of vertex operators on a lattice. In particular, the lattice analogues of operator product expansions and braid relations are discussed. As the…
In his landmark paper, Zhu associated two associative algebras to a vertex operator algebra: what are now called Zhu's algebra and the C_2-algebra. The former has a nice interpretation in terms of the representation theory of the VOA, while…
Let $V$ be a strongly rational vertex operator algebra, and let $g_1, g_2, g_3$ be three commuting finitely ordered automorphisms of $V$ such that $g_1g_2=g_3$ and $g_i^T=1$ for $i=1, 2, 3$ and $T\in \N$. Suppose $M^1$ is a $g_1$-twisted…
A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the…
Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is…
In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their $g$-twisted analogs) are Noetherian. These carry important information about the…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…
We apply the factorization and vector bundle propositionerty of the sheaves of conformal blocks on $\overline{\mathscr{M}}_{g,n}$. defined by vertex operator algebras (VOAs) and give geometric proofs of essential results in the…
Let $\mathcal{M}\subseteq\mathcal{B}\left( \mathcal{H}\right) $ be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight $\tau$ where $\mathcal{B}\left( \mathcal{H}\right) $ is the…
We study a family of modules over Kac-Moody algebras realized in multi-valued functions on a flag manifold and find integral representations for intertwining operators acting on these modules. These intertwiners are related to some…
On the space of bounded analytic functions and the Bloch space on the unit disk, we study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators. Further, we consider the…
We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…
We give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super)algebras originally obtained by Meurman and Primc using a different method. This…
For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules…
In this paper, we investigate the theory of $g$-twisted modules for modular $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebras over an algebraically closed field $\mathbb{F}$ of prime characteristic $p>2$. For a…
We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by $\mathbb{Z}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a…